Kinematics Flashcards
define rigid body
Doesn’t deform under applied forces/moments
Define a body
An element of finite size (unlike a particle)
define spatial motion
bodies/particles are free to move in 3D space
How many degrees of freedom (DoF) are there in spatial motion?
6 degrees of freedom:
- 3 DoF of translation, independent motions in x, y, and z directions
- 3 DoF of rotation, independent motions about x, y, and z axes
define plane motion
bodies/particles are constrained to move in a plane
How many degrees of freedom are there in plane motion?
3 degrees of freedom:
- 2 DoF of translation, independent motions in x and y directions
- 1 DoF of rotation about the axis perpendicular to the plane (z-axis)
how do you measure the degree of rotation of a rigid body?
It’s measured using a line within the body,which is then compared to an external reference line that doesn’t rotate.
Equation for tangential velocity
v = ω r
ω = angular frequency
r = radius
Equation for radial acceleration
a = ω^2 r
ω = angular frequency
r = radius
Equation for tangential acceleration
a = α r
α = angular acceleration
r = radius
How do you find angular acceleration (α)
α = Δω/Δt
Δω = change in angular frequency
Δt = change in time
How do you find angular frequency (ω)
ω = 2π f
= v/r
f = frequency
v = tangential velocity
r = radius
The two types do acceleration experienced by a point with an angular velocity
Tangential acceleration
Radial acceleration (towards centre)
Find the sum of moments about the centre of gravity
ΣM = I α
I = moment of inertia
α = angular acceleration
Calculate the moment of inertia (If)
If = I + mr^2
